Related papers: A shorter proof of Lemma A.6 (arXiv:1005.0768)

We generalize Merton's asset valuation approach to systems of multiple financial firms where cross-ownership of equities and liabilities is present. The liabilities, which may include debts and derivatives, can be of differing seniority. We…

We provide a hand-checkable proof for Lemma 4.9 in the paper "Logical limit laws for minor-closed classes of graphs" by Heinig, Muller, Noy and Taraz.

We provide a critical analysis of the proof of the fundamental theorem of asset pricing given in the paper "Arbitrage and approximate arbitrage: the fundamental theorem of asset pricing" by B. Wong and C.C. Heyde (Stochastics, 2010) in the…

A simple quantitative example of a reflexive feedback process and the resulting price dynamics after an exogenous price shock to a financial network is presented. Furthermore, an outline of a theory that connects financial reflexivity,…

The proof of Theorem 11 of the paper M. Scheepers, Remarks on countable tightness, Topology and its Applications 161 (2014), 407 - 432 relies on Lemma 10 of that paper. The offered proof of Lemma 10 had shortcomings, and I was recently…

We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly…

We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that…

We show that the results of ArXiv:1305.6008 on the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (\emph{hedging options}) are quoted with…

This text highlights issues present in the proof of Lemma 6.10 of the Baumgartner (1943 -- 2011) article "Almost disjoint sets, the dense set problem and the partition calculus" of 1976, and intends to present a correction at the same time…

This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.

We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.

We consider a multi-asset incomplete model of the financial market, where each of $m\geq 2$ risky assets follows the binomial dynamics, and no assumptions are made on the joint distribution of the risky asset price processes. We provide…

A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case

A simple statement and accessible proof of a version of the Fundamental Theorem of Asset Pricing in discrete time is provided. Careful distinction is made between prices and cash flows in order to provide uniform treatment of all…

This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).

We prove an easy version of the minimax theorem with no topological assumption. We deduce from it some domination criteria as well as an application to $p$-summing operators.

In a preceding paper [E.J.ofProb.34,860-892,(2006)], we proved a sewing lemma which was a key result for the study of Holder continuous functions. In this paper we give a non-commutative version of this lemma with some applications.

We give an undergraduate short and simple proof for Zariski's lemma.

We develop a novel framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive the nonlinear…

This article presents an elementary proof of Zorn's Lemma under the Axiom of Choice, simplifying and supplying necessary details in the original proof by Paul R. Halmos in his book, Naive Set Theory. Also provided, is a preamble to Zorn's…